J . Phys. Chem. 1984, 88, 3820-3826
3820
reaction 2. We thus assert that neutral equilibrium water clusters have a negative electron affinity. Conclusions We have been concerned with the energetic stability of small water clusters containing an excess localized electron, considering both the electronic binding energy and the cluster nuclear reorganization energy. The approximation inherent in our approach should be elaborated on. Firstly, we did not consider entropy effects. Water clusters in supersonic beams may be quite hot7b and entropy contributions should be incorporated in a more complete treatment. Secondly, we have considered only one type of excess electron state, namely, the one in which the electron is sufficiently localized, so that the molecules of water are oriented by its presence, resulting in a negative cluster, whose structure is quite different from that of a neutral cluster. It is possible that electrons could be bound to surface states on the outside of large clusters of polar (and even nonpolar) species, as shown by Antoniewicz, Bennett, and Thomspon,Is but such species would be weakly bound, e.g., of the same energy as negative ions of LiCl, LiF, etc.,19s20and would have ultralow energy excitation spectra. For reference, the total binding energy of an electron on LiCl, which has a dipole moment of 7.2 D, is 0.6 eV, but the dipole moment only accounts for about 0.08 eV of this energy. The water octamer studied by Stillinger and David" has a dipole moment of only 4.61 D, and this should have a significantly lower stability and excitation energy. For these reasons that type of surface states is not treated in more detail in this paper. The general conclusions emerging from these model calculations on the energetic stability of (H20); clusters lead to the following conclusions (18) P. R. Antoniewicz, G. T. Bennett, and J. C. Thompson, J . Chem. Phys., 77,4573 (1982). (19) K. D. Jordan and W. Luken, J . Chem. Phys., 64, 2760 (1976). (20) K. D. Jordan, K. M. Griffing, J. Kenney, E. L. Anderson, and J. Simons, J . Chem. Phys., 64,4730 (1976).
(1) Interactions beyond the first coordination layer are essential for the localization of an excess electron. This is apparent from the minimal size n = 6 (4 2) of a cluster, which is energetically stable with respect to nHzO e. The crucial interactions beyond the first coordination layer in the cluster are analogous to the "long-range" electron-medium interactions in the dense fluid, which are crucial for the energetic stability, spectra and localization, and dynamics of excess electrons in These interactions in a fluid are in a sense cooperative, depending on the fluid density. The calculations on (H,O),- clusters provide insight into the nature of these cooperative effects in fluids, as explored from the microscopic point of view. (2) The localization of an excess electron in a preexisting equilibrium cluster is accompanied by large configurational changes within the cluster, resulting in a considerable cluster rearrangement energy. (3) An excess electron will not bind to a preexisting neutral, stable, equilibrium, water cluster. This conclusion, which rests on the negative electron affinity estimated for stable clusters (Table II), is in accord with the recent experimental works,9 which demonstrated that electrons do not attach to preformed water clusters in the low-pressure domain of supersonic jets. (4) Metastable (H,O), (n 1 6) neutral clusters are required for the initial localization of an excess electron. These negative small clusters once formed can subsequently attach additional water molecules. (H,O); ( n 2 11) clusters were experimentally observedsb when a water vapor in an expanding supersonic jet is mixed with electrons. These experimental conditions favor electron attachment to small metastable water clusters.
+
+
Acknowledgment. This work is partially supported by the Department of Energy (Contract DE-AS05-77ER05399) in the Office of Basic Energy Sciences, Solar Photochemistry Division awarded to N.R.K. Registry No. H,O, 7732-18-5; (H,O)-, 12259-30-2.
Thermodynamics, Electrochemistry, and Kinetics of Sodium-Ammonia Solutions U. Schindewolf Institut fur Physikalische Chemie und Elektrochemie der Universitat Karlsruhe, Karlsruhe, West Germany (Received: August 24, 1983)
EMF measurements are reviewed which in combination with some extrathermodynamic assumptionsyield the thermodynamics of solvated electrons in liquid ammonia. We think the best experimental data for the solvation enthalpy and entropy at -40 OC are AHo = -95 & 10 kJ/mol and ASo= 154 i 20 J/(mol K). The individual data for the electron are used to outline the energetics of the solution process of a metal, its solubility, and the absolute potential difference between a metal and its saturated solution. The concept of absolute electrode potential helps us to understand the electrochemical response of a metal electrode to solvated electrons or to any redox system. Kinetic data are reported for the reaction e- + H20in ammonia, casting some doubts on the estimated thermodynamics of the hydrated electron which are based on its kinetics in water. Thermodynamicsof the solid sodium cryptand compound Na'CNa- is given which is easily prepared from a sodium-ammonia solution. Finally, the experimental findings of another phase instability above the normal miscibility gap of sodium-ammonia solutions will be reported.
will return to the original aim and restrict ourself entirely to some Introduction physicochemical properties of the sodium-ammonia system. Colloque Weyl 1organized by Lepoutre and Sienko and held First a short review of the thermodynamics of sodium-ammonia 1963 in Lille' was devoted to physicochemical properties of solutions and solvated electrons will be given. On the basis of this Ever since, the topics of c~~~~~~~~ metal-ammonia solutions, the energetics of a metal electrode in contact with a solvent will Weyl have expanded in general to electrons in fluid phases be discussed. This leads to the concept of the absolute equilibrium In this paper we including other solvents, metallic systems, potential difference between the metal electrode and the solvent; it shows that the metal ions as well as solvated electrons are determining the electrode potential. Then some experimental (1) G. Leputre and M. J. Sienko, Ed., "Metal-Ammonia Solutions-,w, material will be presented on the kinetics of the solvated elecA. Benjamin, New York, 1964. 0022-3654/84/2088-3820$01.50/0
0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 17, 1984 3821
Sodium-Ammonia Solutions
1800 1
tron-water reaction in ammonia, casting some doubts on the thermodynamic data of the hydrated electrons which are based on its reaction kinetics in water. Further thermodynamic studies indicate another phase instability for the sodium-ammonia solutions above the normal miscibility gap. These experimental results add new mysteries to metal-ammonia solutions rather than solving the old ones. Thermodynamics of Solvated Electrons in Ammonia Vapor p r e s s ~ r eand ~ , ~E M F measurements4-' with metal-ammonia solutions have extensively been used to obtain the thermodynamics of the solvent ammonia and the dissolved metal. For E M F measurements the best arrangement is the ~ e l l * 9 ~ Pt(Na1INa+-.ammonia-e-lPt
(1)
K r
-
Na+
+ e-
Na+ + 2e- s (Na+e22-)
(4)
AH"(4) = -30 f 2 kJ/mol
-
h
t
1/2H1+ NH,
(5)
*
AH"(5) = -179 6 kJ/mol AS"(5) = 26 f 6 J/(mol K)
So far the data give only the sum of the thermodynamic quantities of electrons and cations (Le., Na+ e-). To get the individual data for the solvated electrons extrathermodynamic assumptions have to be made. In several attempts which included evaluating heats of reactions and heats of solution of salts,"J2
+
h
c erylene e n
a
e
->
1200
Anthracene
bH
l.ld0-178
5 lo2' -165
8 10'' -141
E
8 1019 -1 38
u
-
LL
I
2 10l6 -130
u 600
2 lo'* -107410" -112 2 1010 -1 00
I 0
Equivalence point added sodium Figure 1. Potentiometric titration curves of aromatic hydrocarbons ( 1 X M) in liquid ammonia with sodium-ammonia solutions, using the electrochemical cell of eq 1 at -40 O C . I 4
EMF measurements, and theoretical data,13the solvation enthalpy of the electron in ammonia has been given to be between 46 f 16 and 164 f 19 kJ/mol. We tried another way based on the reaction of dissolved aromatic molecules A with solvated electrons leading to their radical anions A- l 4 e- A Athe thermodynamics of which with nine different aromatic hydrocarbons we could study with high precision by E M F measurements with the cell described in eq l . Figure l displays potentiometric titration curves of dissolved aromatics with a sodium-ammonia solution. By applying the Born-Haber cycle
+
e-
+
l-AHo(e-I
in which the cation serves to reduce the Coulomb repulsion of the two electrons. Finally, from the standard electrode potential of the sodium electrode relative to the hydrogen electrode'O (EO(Na,N) = -1.82 f 0.02 V) that of the solvated electron could be extracted (Eo(e-,H) = -1.91 f 0.02 V, (-40 "C) which describes the reaction
+ NH4+
p
(3)
where E " ( 2 ) = -AGo(2)/F = -0.09 V standard EMF; a(i) are the activities of sodium ions and solvated electrons; R , T , and F are the ideal gas constant, absolute temperature, and Faraday constant. From this the partial molar data Ho = 23 f 2 kJ/mol and So = 107 f 4 J/(mol K) for dissolved sodium (Na' + e-) under standard conditions are obtained (extrapolated from high dilution where the system has ideal behavior; here and in the following, the hypothetic ideal standard state is 1 M; the temperature is -40 "C; the enthalpy of the pure elements under standard conditions is set zero; and the entropy is the absolute entropy). Furthermore it was shown that the transition to the metallic state is exothermic and exentropic and that the spinpairing process can best be described by the exothermic equilibrium
e-
a
(2)
E(2) = E"(2) - R T / F In (a(e-)a(Na+)) = -AG(2)/F
K(4) = 9 X IO4 M-2
q
2.1ds -173
the left part of which with the solid ion conductor sodium palumina (represented by 11) responds to sodium ions and the right to solvated electrons. The E M F of the cell gives the osmotic work or the free energy change for the dissolution reaction of solid sodium which leads to solvated sodium ions and solvated electrons Na(s)
1
I
1
e-
+
A - A
1-
A
€(A)
AH"(P)
AH'(R)
1
gas phase
A H O( A- )
A-
liquid phase
( W ( i ) is the solvation enthalpy of species i; E(A) the gas-phase electron affinity of hydrocarbons; A P ( R ) the reaction enthalpy in ammonia) and the Born a p p r o x i m a t i ~ n 'for ~ the enthalpy change when charging a large spherical molecule in a dielectric medium (which is the difference of the solvation enthalpies of the molecule A and its anion A-, assuming no specific interaction between the ion and the solvent), the solvation enthalpy and by a corresponding treatment the solvation entropy of the electron in ammonia are obtained: AHo(e-) = -95 f 10 kJ/mol
ASo(c-) = 154 f 20 J/(mol K) From these follow the partial molar quantities of the solvated electron Ho(e-) = -90 f 10 kJ/mol So(e-) = 169 f 20 J/(mol K)
(2) P. R. Marshall, J . Chem. Eng. Data, 7, 399 (1962). (3) U. Schindewolf and M. Werner, Ber. Bunsenges. Phys. Chem., 81, iooa (1977). (4) C. A. Kraus, J. Am. Chem. SOC.,36, 864 (1914). (5) H.A. Laitinen and C. J. Nymann, J . Am. Chem. SOC.,70, 2241 11948). (6)J. B. Russel and M. J. Sienko, J . Am. Chem. SOC.,79, 4051 (1957). (7) J. L. Dye, ref 1, p 137. (8) K. Ichikava and J. C. Thompson, J . Chem. Phys., 59, 1680 (1973);62, 4958 (1975). (9)U. Schindewolf and M. Werner, J. Phys. Chem., 84, 1123 (1980). ~
Thus the solvation enthalpy is well within the wide scatter of (10) M. Werner und U. Schindewolf, Ber. Bunsenges. Phys. Chem., 84, 547 11980). ((1) L.'V. Coulter, J . Phys. Chem., 57, 533 (1953). (12) N . M. Senozan, J. Inorg. Nucl. Chem., 35, 727 (1973). (13) J. Jortner, J. Chem. Phys., 30, 839 (1959). (14) W. Gross and U. Schindewolf,Ber. Bunsenges. Phys. Chem., 85, 112 (1981). (15) M.Born, Z . Phys., 1, 45 (1920).
3822 The Journal of Physical Chemistry, Vol. 88, No. 17, 1984 Enthalpy lkJ/moll
Metal
Solution
Entropy lkJ/rnolI
Metal
Solution
Schindewolf
Free Enthgipy IkJlmoll
Met01
Csl(Cs+...ammonia...e-lPtlCs
(7)
it is obvious that the platinum acts as a semipermeable membrane for electrons. Both membranes prevent the direct dissolution of the cesium in the solvent. At electrochemical equilibrium Aqo(i) = Apo(i) z(i)FApo(i) = 0 (8)
SOI"!lO"
+
AH*=lO
AS'=Sl
(As(i) is the electrochemical potential difference; Ap(i) the chemical potential difference of the cesium ions or the electrons between the solution and the metal; Ap(i) the electrical (Galvani) potential difference between the solution and the metal; z(i) the cation or electron charge) we have two potential drops at the two sides of eq 7 which add up to the measurable EMF Apo(i) = -Afio(i)/(z(i)F)
AG'r-9
Eo(Cs) = Apo(Cs+) - Apo(e-)
Thermodynamic Data for Cesium Metal ond Cesium dissolved ammonia
Figure 2. Diagram of thermodynamic data of Cs' ions and electrons in Cs metal and in liquid ammonia (standard state 1 M ideal sol~tion;'~ the entropy is in J mol-' K-I).
literature data, and it as well as the solvation entropy or the free enthalpy of solvation ( N -1.36 V) are close to the data estimated by Lepoutre and J o r t n e P and later adopted by Bard." Electrochemistry of Metallic Electrodes The thermodynamic data of solvated electrons, solvated metallic cations, and the corresponding metals allow us to construct energy diagrams from which the "absolute" electrode potentials can be obtained. We consider cesium. The electron work function of cesium1*(1.81 V = AGO = A P = 175 kJ/mol at 0 K) describes the energy necessary to transfer an electron from the metal to vacuum. Therefore the enthalpy of the electron in the metal will be -175 kJ/mol at 0 K. The same value can be used at normal temperatures because the Fermi distribution will be disturbed only slightly. According to convention the enthalpy of the pure elements at standard condition (-40"C) is zero; therefore the enthalpy of the cesium ion in the metal is 175 kJ/mol. The entropy of the cesium ions is that of the metallic cesium (77 J/(mol K)) because the electrons hardly contribute to the entropy. With these and the data for cesium ionslg and electrons in solution we construct the diagrams in Figure 2. The solution process is endothermic, because the gain of enthalpy in transferring the cation from the metal into the solution is overcompensated by the enthalpy requirement to transfer the electron. However, combination of the entropy and enthalpy data yields a negative change of free enthalpy for the dissolution process, in which the transfer of the cation is the driving force, the electron being dragged along because of electroneutrality against its chemical potential gradient (it should be noted that the unknown surface potential of the liquid and the uncertainty of the work function might lead to slightly different data, which, however, will not invalidate the given conclusion). From AGO = -9 kJ/mol and AG = 0 = AGO R T In (a(equi1, e-)a(equil, Cs+)) at solution equilibrium (compare eq 3) it follows that the ideal solubility product of cesium K(Cs) = a(equi1, e-)a(equil, Cs+) is around 100 M2. In the electrochemical cell of eq 1 with cesium instead of sodium in which the metal is separated from the hypothetical ideal 1 M metal solution by an ion conducting semipermeable membrane represented by 11, the standard EMF is given by the difference of the standard potentials of the cesium electrode and the electron electrode both relative to the normal hydrogen electrode
+
Eo(Cs) = -AGo/F = Eo(Cs,H) - Eo(e-,H)
(6)
The absolute potentials between the electrodes and the solution are not known. If the electrochemical cell is written in the equivalent formulation (16) G. Lepoutre and J. Jortner, J . Phys. Chem., 76, 683 (1972). (17) F. A. Uribe, T. Sawada, and A. J. Bard, Chem. Phys. Lett., in press. (18) "Handbook of Chemistry and Physics", The Chemical Rubber Co., Cleveland, OH, 1973. (19) U. Schindewolf, Ber. Bunsenges. Phys. Chem., 86, 887 (1982).
(9)
In case of cesium with data of Figure 2 we obtain Apo(Cs+) = 0.57 V, Apo(e-) = 0.48 V, and Eo(Cs) = 0.09 V (standard activities, -40 "C). If the metallic cesium is partly covered with a cation permeable membrane and partly with an electron permeable membrane and contact is made between them with a solution (i.e., short circuiting M1(7)), the electrochemical equilibrium is no Ionger given because we can not have two different potential drops (Ap(Cs+) and Ap(e-)) between the solution and the metal. Cations and electrons will pass through the membranes, increasing the activities or chemical potentials of both species until at saturation the chemical potential differences cancel (AG = 0) and an electrical equilibrium potential (Ap(equi1)) between solution and metal is established Ap(equi1) = -Ap(equil,Cs+)/F = Ar(equil,e-)/F
(10)
The same potential of course is developed when the metal is in direct contact with the saturated solution; we might call it the "absolute" equilibrium potential. For cesium in ammonia Acp (equi1,Cs) = 0.525 V. In comparison, for silver (Eo(Ag,H) = 0.8 V; electron work function 4.73 V), we find a solubility product of K(Ag) = M2 (equilibrium activities a(equil,Ag+) = a(equi1,e-) = M) and an equilibrium potential of Acp(equi1,Ag) = 2.03 V (the equilibrium potentials are given with the uncertainty of the surface potential of ammonia and of the work function of the metals). Because the activities of cations (M') and electrons in a solution in contact with a metal (M) are given by the solubility product K(M) = a(M+)a(e-) = a(equil,M+)a(equil,e-), a change of the activity of one of them will change that of the other and will change the electrode potential which is F/RT(Ap
- Ap(equi1)) = -In -In
am+) a( equil,M+)
--
4e-) K(M) = In (11) a(equil,M+)a(e-) a( equi1,e-)
i.e., the Nernst relation is followed by cations as well as by electrons; both are potential-determining particles. This concept makes it understandable that any insoluable electrode will respond to solvated electrons and to all redox equilibria Re
+ Ox+ + e-
(12)
which always can be formulated with solvated electrons as a reaction partner in the solution. The potential of the electrode is K(Re,Ox)a(Re) A p = Ap(equi1) + R T / F In (13) a(equi1,e-)a(Ox) as found by inserting the expression for the equilibrium constant K(Re,Ox) of redox reaction 12 into eq 11. This concept includes, as pointed out already by Frumkin20 and Trasatti21 that the (20) A. N. Frumkin and B. B. Damaskin, Dokl. Akad. Nauk. USSR, 221, 395 (1975).
Sodium-Ammonia Solutions
The Journal of Physical Chemistry, Vol. 88, No. 17, I984
equilibrium between a metal and a solution is not
M
M+ + e,-
(14)
with the electron left in the metal, but
M s M+ + e-
Kinetics of the Electron Reaction with Water in Ammonia The hydrated electron22is known to react very fast with water in a bimolecular process
k=5
X
-
+ 2H20
2e-(aq)
H2 + 2 0 H -
(16)
IO9 M-’ s-l AHo = -397 kJ/mol ASo = -12 J/(mol K)
(the thermodynamic data of this section are taken from ref 19) and in a monomolecular process e-(aq)
+ H20
-
H
+ OH-
k = lo3 s-I AHo = 10 kJ/mol ASo = -48 J/(mol K)
-
+ 2NH3
AHo = -168 kJ/mol
H2
+ 2NH2-
(18)
ASo = -466 J/(mol K)
neither this bimolecular process nor the monomolecular analogue of reaction 17 e-(am)
+ NH3
AHo = 125 kJ/mol
-
H
+ NH2-
(19)
ASo = -272 J/(mol K)
are known. The metal-ammonia solutions are practical indefinitely stable probably due to the very positive absolute entropy of the ammoniated electron (So = 169 J/(mol K) in contrast to the hydrated electron So = 13 J/(mol K)23) which leads to a very negative activation energy or a small rate constant according to transition-state t h e ~ r y . ’ ~ ,With ~ ~ , the ~ ~ same entropy argument we should expect that the ammoniated electron also will not react with water although again the bimolecular process 2e-(am)
+ 2H20
AHo = -314 kJ/mol
-
H2 + 2 0 H -
(20)
So = -554 J/(mol K)
is favorable; the monomolecular reaction e-(am)
+ H20
AHo = 52 kJ/mol
H
+ H 2 0 F! NH4+ + OHe-(am) + NH4+- 1/2H2+ NH,
+ OH-
NH,
(22) (23)
By applying the concept of the quasistationary state for ammonium ions he estimated the rate constants for the individual reaction steps as k(22) = 7 X k(-22) = 2 X lo6; k(23) = 4 X lo6 (all in M-’ s-l and at -34 “C). Reaction 23 of course should be replaced by e-(am)
+ NH4+
AHo = 30 kJ/mol
-
H
+ NH,
(24)
ASo = -12 J/(mol K)
followed by fast hydrogen recombination. Our recent flash photolysis experiments of ammonia solutions with varying concentrations of water and cesium hydroxide (OH+ hu e-(am) + OH; OH scavenged by molecular hydrogen) makes this reaction sequence rather unlikely.28 The rate of electron disappearance in the concentration range from to M (measured by spectral photometry) strictly follows the rate law
-
d[e-]/dt = -k[e-] [ H 2 0 ]
followed by fast hydrogen recombination. Although thermodynamics also favor the decomposition of electrons in ammonia 2e-(am)
in a detailed mechanistic study by D e ~ a l d . ~ ’ Dewald measured the time dependence of the electrical conductivity of dilute sodium-water-ammonia mixtures and concluded that the reaction proceedes via ammonium ions formed in an equilibrium reaction between water and ammonia
(15)
where the electron also is transferred to the solution and solvated. It also quantitatively expresses the “Losungsdruck der Metalle” (which describes according to Nernst the tendency of a metal to go into solution) by the solubility product which is the equilibrium constant of, e&, reaction 2 or 15.
3823
(21)
So = -316 J/(mol K)
is less likely because it is endothermic. However, the decomposition of electrons in ammonia by added water is known to proceed, as shown qualitatively by pulse r a d i o l y s i ~and ~ ~quantitatively ~~~ (21) S. Trasatti, Adu. Electrochem. Electrochem. Eng., 10, 213 (1977); A. D. Battisti and S . Trasatti J . Electroanal. Chem., 79, 251 (1977). (22) E. J. Hart and M. Anbra, ‘The Hydrated Electron”, Wiley-Interscience, New York, 1970. (23) J. Jortner and R. M. Noyes, J . Phys. Chem., 70, 770 (1966). (24) G. Leputre and A. Demortier, Ber. Bunsenges, Phys. Chem., 75,647 (1971). (25) J. L. Dye, M. G. DeBacker, and L. M. Dorfmann, J. Chem. Phys., 52, 6251 (1970).
with a rate constant of k(25) = 0.3 f 0.05 M-’ s-l (-35 “C) and an activation energy of E , = 10 f 2 kJ/mol. Since hydroxide ions do not influence the rate, equilibrium 22 cannot be part of the reaction (furthermore, the equilibrium constant K(22) is about 10l2times smaller29and therefore the ammonium ion concentration is much smaller than assumed by D e ~ a l d ; ~to’ give the same reaction rate then the rate constant k(23) should be much larger than deduced and later confirmed by Dewald30). However, these results do not help us understand the reaction of the ammoniated electron with water. The rate law would be consistent with reaction 21 leading to hydrogen atoms. But since this reaction is endothermic (AH’ = 52 kJ/mol), the activation energy should be larger than the reaction enthalpy, at least 60 kJ/mol instead of the measured 10 kJ/mol. Thus we assume the electron undergoes an exothermic reaction to an unknown intermediate which in turn forms hydrogen: e-(am) 2X
-
-
+ H20 X H2 + 2 0 H -
(26) (27)
From the measured rate constant and activation energy an activation entropy of -220 J/(mol K) is calculated with the transition-state theory, which again is very negative in accordance with the very positive entropy of the ammoniated electron. At first glance this hypothesis might be rather speculative. But it finds support from other experiments. Walker3*generated hydrated electrons by flash photolysis. Up to 1 ms after the flash when the normal reactions 16 and 17 had proceeded, another flash (A > 280 nm; filtered not to contain any short wave components which would photogenerate further electrons) revived the hydrated electrons. After a longer delay or when the primary electrons had reacted with other substrates, e.g., oxygen, the second flash was ineffective. In similar experiments Hart32could revive solvated electrons by filtered light pulses (26) R. Olinger and U. Schindewolf, Ber. Bunsenges.Phys. Chem., 75,693 (1971). (27) R. Dewald and R. V. Tsina, Chem. Commun., 647 (1967); J . Phys. Chem., 72, 4520 (1968). (28) T. Telser and U. Schindewolf, Ber. Bunsenges. Phys. Chem., in press. (29) U. Schindewolf and H. Schwab, J . Phys Chem., 85, 2707 (1981). (30) J. M. Brooks and R. Dewald, J . Phys. Chem., 75, 986 (1971). (31) N. Basko, G. A. Kenney, and D. C . Walker, Chem. Commun., 917 (1969); N. Basko, G. A. Kenney-Wallace, S . K. Vidyarthi, and D. C . Walker, Can. J . Chem., 50, 2059 (1971).
Schindewolf
3824 The Journal of Physical Chemistry, Vol. 88, No. 17, 1984 in solutions in which by continuous photolysis a low steady-state concentration of solvated electrons was maintained. Walker explains the results as an indication that two electrons combine in a second-order reaction to an electron pair as a longer-living precursor of hydrogen (2e- e22- H2) which by photolysis is split into hydrated electrons again whereas Hart postulates a dissociable complex involving a sodium ion and a solvated electron (Na+e-) as the intermediate. However, we also might assume that the hydrated electron follows the reaction sequence analogue (26), leading to an unknown X which can be photolyzed again or forms hydrogen. Since we do not know anything about this intermediate X which we postulate for the electron-water reaction in ammonia and which probably is formed in the same reaction in water we have to admit that we still do not understand this reaction as Anbar and Hart stated already in 1970.22 However, one concluding remark might be made. If really the solvated electron in its reaction with water forms an unknown intermediate X and not hydrogen atoms than the thermodynamic data for the hydrated electron should be corrected. They are based on the measured kinetics of reaction 17 leading to hydrogen atoms and the reverse reaction (k(-17) = 2 x 107 M-' s-1 ). From the two rate constants the equilibrium constant is calculated as K(17) = k(17)/k(-17) and with AG'(17) = -RT In K(17) = p"(H) p"(OH-) - p 0 ( H 2 0 ) - po(e-) and the known chemical potentials po(i) of the other reaction partners the data for the hydrated electron are estimated23( H o = -153 kJ/mol, So = 13 J/(mol K) at 25 "C). If, however, reaction 17 has to be replaced partly or completely by the analogue of reaction 26 then the rate constant k( 17) must be smaller than the measured rate constant for the disappearance of electrons; consequently, the chemical potential of the hydrated electrons should be more negative and its normal potential relative to the hydrogen electrode less negative than the reported value,22E"(e-,H) = -2.77 f 0.1 V. Thermodynamics of Solid Sodium Compounds -+
-+
+
The electrochemical cell in eq 1 allows us to measure the thermodynamics of solid compounds containing metallic sodium. We applied it to Na'CNa- (Dye crystals;33 C, cryptand). For the preparation of Dye crystals solid sodium (3 X mol) and mol) are put in the cell. an excess of solid cryptand (2 X Ammonia is distilled on and evaporated off again to divide the sodium finely. Then a mixture of ethylamine and methylamine ( 5 mL) and T H F (1 mL) is distilled into the cell at 0 "C. After the solution is cooled, the gold-colored Dye crystals precipitate; the solution remaining is deep blue. The E M F of the cell with dispersed Dye crystals and solid cryptand (Le., saturated with both) directly yields the free energy of formation of the solid compound from solid sodium and solid cryptand 2Na(s)
+ C(s)
-
Na+CNa-(s)
Equation 28 is the sum of two times eq 2 (Na(s) and 2Na+
120 I
+ 2e- + C(s)
-
(28) Na+ + e-)
Na+CNa-(s)
(29)
The standard free energy change of reaction 29 is given by the solubility product of Dye crystals (activities of the solids are unity) AG0(29) = R T In K(DC) = 2 R T In (a(e-)a(Na+))
(30)
that of reaction 2 by the standard EMK of cell 1 AGo(2) = -E0(2)F Inserting eq 30 and 31 into eq 3 we obtain E = -AG0(2)/F- AGo(29)/2F = -AG0(28)/2F
(31) (32)
Hence the EMF of the cell in the presence of solid cryptand and solid Dye crystals gives the free energy of formation of these crystals from the two components, irrespective of the solvent used. ~
(32) C. Gopinathan, E. J. Hart, and K. H. Schmidt, J. Phys. Chem., 74, 4169 (1970).
Figure 3. EMF of the cell in eq 1 with added Dye crystals and solid cryptand (0)33 as a function of temperature. (Note Added in Proof the upper curve with its data points has no significance.)
The E M F and its temperature dependence in Figure 333 extrapolated to 298 K yield AGO = -7 f 1 kJ/mol, AHo = -34 f 2 kJ/mol, and ASo = -90 f 8 J/(mol K). The data confirm the experience that Dye crystals are stable only at low temperatures and will decompose into its components at higher temperatures (AGO becoming more positive with increasing temperature). If we apply Born-Haber cycles and the data given, it will now be possible to reveal the thermodynamics of the many alkali alkalides and electrides which have been synthesized by Dye.35
A New Phase Instability Above the Normal Miscibility Gap? In recent heat capacity experiments on sodium-ammonia solutions in the range of the nonmetal-metal transition, we3*observed anomalies which cannot be described with our present knowledge of metal-ammonia solutions. Starting at low temperatures (see Figure 4) in the normal miscibility gap the heat capacity is a smooth function of temperature (Figure 5 ) . However, it takes up to 24 h until thermal equilibrium after introduction of heat is established because the concentrations of the two equilibrium phases must change and can do so only by slow diffusion processes. When by further temperature increase the miscibility gap is left, the heat capacity has a sharp break and thereafter changes smoothly with temperature. In homogeneous solutions thermal equilibria are obtained within 1 h. But by heating further two more jumps in the heat capacity occur (Figure 5) at two distinct temperatures between which again a long equilibrium time is observed. These additional anomalies indicate another phase instability above the normal miscibility gap. Later we tried to confirm the results by E M F measurements with the cell arrangement shown in (1) and by conduction meas u r e m e n t ~both , ~ ~ as a function of temperature. When the temperature scan was too fast (>1 K/min) only a smooth curve was obtained, but at scan rates below 0.1 K/min going up and down both the E M F and the conduction measurement also revealed changes in slope which can be taken as additional evidence for (33) U. Schindewolf, L. D. Le, and J. L. Dye, J . Phys. Chem., 86, 2284 (1982). (34) Deleted in proof. (35) J. L. Dye, Angew. Chem., Inl. Ed. Engl., 18, 587 (1979); J . Phys. Chem., 84, 1084 (1980). (36) Deleted in proof. (37) Deleted in proof. (38) V. Steinberg, A. Voronel, D. Linski, and U. Schindewolf, Phys. Reu. Lett., 45, 1338 (1980). (39) R. Winter, U. Schindewolf, and A. Voronel, "Ionic Liquids, Molten Salts and Polyelectrolytes", Lecture Notes in Physics 172, Springer, Heidelberg, 1982.
The Journal of Physical Chemistry, Vol. 88, No. 17, 1984 3825
Sodium-Ammonia Solutions
293
210
283 200 -
1
273 !
\
263
190
Y
0
\
I-
,
!
I 8
253
Figure
243 Li6
233
I 9
I
2 2:
3
4
5
6 MPNa
I
8
L?, ~i~
___c
Figure 4. Phase diagram of sodium-ammonia solutions: lower curve, normal miscibility gap; upper curve, new phase instability measured by (Note heat capacity (X), E M F (A),and conduction experiments (.).3s*3g Added in Proof the data points 0 and have no significance.)
- TIK2L3
253
263
273 NH,- evaporation
Figure 7. Flow scheme for the lithium isotope enrichment process.
application of it. We found that at -75 OC the 6Li/7Li isotope ratio in the concentrated metallic phase is about 1% larger than in the dilute electrolytic phase.43 This can be described by an isotope exchange equilibrium %(el)
I
223
I
233 2L3 253 -TIKFigure 5. Heat capacity of a 4.6 (a) and 6.3 (b) MPM sodium-ammonia solution (about 5 mL) under its normal vapor pressure. Dashed lines indicate those temperatures at which the instabilities begin or end.38
this new two-phase region which is shown in Figure 4 (data from heat capacity (X), from E M F (A), from conduction ( 0 ) . Although we cannot discuss the new instability any further we feel that it might be an experimental proof of a general t h e o r P 4 l predicting two critical points in strongly ionized or metallic systems as proposed originally by Landau.42 Lithium Isotope Separations At low temperatures the metal-ammonia solutions exhibit a miscibility gap with two equilibrium phases of widely different metal concentrations (Figure 6 ) . Here we will give an interesting (40) W. Ebeling and R.Sandig, Ann. Phys. 28,289 (1973); W. D. Kraeft and D. Kremp, "Theory of Bound States and Ionization Equilibrium in Plasmas and Solids", Akademie Verlag, Berlin, 1976. (41) M. Gitterman and V. Steinberg, Phys. Reu. A, 20, 1236 (1979). (42) L. Landau and G. Zeldowich, Acta Physicochim. USSR,18, 194 (1943).
+ 7Li(met)
7Li(el)
+ %(met)
(33)
with an equilibrium constant or separation factor of K = 1.01; this is in parallel to the corresponding 6Li/7Li exchange equilibrium between mercury and an organic solvent with K = 1.02.44 Although the separation effect is rather small it can be made use of for 6Li enrichment by multiplication of the elementary separation effect in a countercurrent flow of the two phases (countercurrent extraction). The enriched isotope 6Li might be of interest for controlled nuclear fusion based on the overall reaction
2D+ 6Li
-
24He
(34)
with an energy release of 22 MeV. The countercurrent flow can be realized in a simple process: the lower part of the extraction column is filled with a dilute lithium solution of higher density, the upper part with a concentrated solution of lower density (Figure 7). If ammonia is distilled off from the dilute solution at the bottom of the column droplets of the concentrated solution will be formed because of the miscibility gap. These droplets move upward in the column due to their smaller density. Condensation of the ammonia into the concentrated solution on the top of the column leads-again because of the miscibility gap-to droplets of dilute solutions which (43) U. Schindewolf, Nachr. Chem. Tech. Lab., 28, 580 (1980). (44) G. N. Lewis and R. MacDonald,J . Am. Chern. SOC.,58,2519 (1936).
J. Phys. Chem. 1984, 88, 3826-3833
3826
move down. Thus the separation effect of eq 33 will be repeatedly established along the countercurrent column leading to an enrichment of 6Li on its top with an enrichment factor which increases exponentially with column length. A plant for the 6Li production for a 2.5-GW (thermal) fusion reactor (600 g of 6Li/day) easily could be combined with that for the production of the necessary deuterium (200 g of D/day) which is also based on an exchange process in liquid ammonia.4s Both installations hardly exceed the dimensions of the bell tower of a small village church and would yield nuclear fuel on a cost level of a few percent of the value of the produced electrical energy. The deuterium enrichment process which also has its origin in fundamental research on metal-ammonia solutions46already is (45) S. Walter and
U.Schindewolf, Chem. Ing. Tech., 37,
1185 (1965).
in operation for the large-scale production of heavy water?' The 6Li-enrichment process is being developed in our laboratory. Thus the purely academic work on the metal-ammonia solutions has lead to a spinoff which one day might yield the unlimited nuclear fuel of the future.
Acknowledgment. The experimental work of our laboratory mentioned in this review has been supported by the Deutsche Forschungsgemeinschaft and the Fonds der chemischen Industrie. We gratefully acknowledge this support. Registry No. Sodium, 7440-23-5; ammonia, 7664-41-7. (46) W. K. Wilmarth and J. C. Dayton, J . Am. Chem. SOC.,75, 4553 (1953). (47) E. Nitschke and S. Walter, Chem. Eng. World, 1, 54 (1970).
Behavior of n-Type and p-Type Silicon in Anhydrous Liquid Ammonia. Solvated Electron Generation: A Supraband-Edge Reaction M. Herlem,* D. Guyomard, C. Mathieu, Laboratoire de Chimie Analytique des milieux rPactionnels, ESPCI, 75231 Paris CZdex OS, France
J. Belloni, Laboratoire de Physicochimie des Rayonnements, Universitt? de Paris-Sud, 91 400 Orsay, France
and J. L. Sculfort Laboratoire d%lectrochimie Interfaciale du CNRS, 921 90 Meudon, France (Received: August 24, 1983; In Final Form: March 1 , 1984)
The behavior of n-type and p-type silicon electrodes (single crystal (100)) is studied in anhydrous basic liquid ammonia with variable solvated electron concentration. In dilute medium, Fermi level pinning on the surface states occurs and the photoelectrochemical cell p-Si/NH3 + KBr (0.1 mol dm-3) + NH2- (2 X lo-' mol dm-3) + e;/counterelectrode delivers a large V, (more than 0.5 V). In concentrated medium ([e;] > 2 X mol dm-3) the strong interaction of e; species toward the SC surface creates a thin conductive layer on the surface which gives a new interface state distribution. Then no photoeffects occur at n-Si or p-Si electrodes.
Introduction Numerous papers concern the behavior of n-type or p-type The nonaqueous silicon in aqueous or nonaqueous (1) D. Laser and A. J. Bard, J. Phys. Chem., 80, 459 (1976). (2) G. Nagasubramanian, B. L. Wheeler, F. R. F. Fan, and A. J. Bard, J . Am. Chem.Soc., 129, 1742 (1982). (3) G. Nagasubramanian, B. L. Wheeler, F. R. F. Fan, and A. J. Bard, J . Am. Chem. SOC.,130, 1680 (1983). (4) K. D. Legg, A. B. Ellis, J. M. Bolts, and M. S.Wrighton, Proc. Narl. Acad. Sci., U.S.A.,74, 4116 (1977). ( 5 ) A. J. Bard, A. B. Bocarsly, F. R. F. Fan, E. G. Walton, and M. S. Wrighton, J . Am. Chem. SOC.,102, 3671 (1980). (6) J. N. Chazalviel, Surf. Sci., 88, 204 (1980). (7) J. N. Chazalviel, J . Electrochem. SOC.,127, 1822 (1980). (8) J. N. Chazalviel, J . Electrochem. Soc., 129, 963 (1982). (9) J. N. Chazalviel and T. B. Truong, J . Electroanal. Chem., 114, 299 (1980). (10) J. N. Chazaviel and T. B. Truong, J. Am. Chem. SOC.,103, 7447 (1981). (1 1) J. A. Turner, J. Manassen, and A. J. Nozik, Appl. Phys. Lett., 37, 488 (1980). (12) B. L. Loo, K. W. Frese, and S. R. Morrison, Appl. Surf.Sci., 8,290 (1981).
0022-3654/84/2088-3826$01.50/0
solvents were used to avoid water or oxygen traces which allow the growth of SiO, or SiOz thin layer on the silicon. This layer seems to play an important part in the redox charge transfer process at the interface, in this way, different results obtained with n-type and p-type silicon were explained by either partial or complete Fermi level pinning,'-1° an inversion mechanism," or interface states arising from the oxide Using oxide-free silicon electrodes in anhydrous medium, we were able to show the influence of pH on the flat-band potential of the semicond~ctor.'~ This pH influence was recently observed (13) M. J. Madou, B. L. Loo, K. W. Frese, and S.R. Morrison, Surf. Sci., 108, 135 (1981). (14) D. G. Canfield and S. R. Morrison, Appl. Surj. Sci., 10,493 (1982). (15) D. Guyomard, M. Herlem, C. Mathieu, C . Miossec, and J. L. Sculfort, J. Electroanal. Chem., 138, 435 (1982). (16) G. Van Amerongen, M. Herlem, R. Heindl, D. Guyomard, and J. L. Sculfort, J . Electrochem. SOC.,129, 1998 (1982). (17) P. Brondeel, M. Madou, W. P. Gomes, P. Hanselaer, and F. Cardon, Solar En. Mater., I, 23, 33 (1982). (18) H. J. Byker, V. E. Wood, and A. E. Austin, J . Electrochem. Soc., 129, 1982 (19821. (l9) A. Heller, H. J. Lewerentz, and B. Miller, J . Am. Chem. SOC.,103, 200 (1981).
0 1984 American Chemical Society
